summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/metapost/byrne/byrne-latex.tex
blob: bbd12af27e0e1b42b8f628eb5a74e62eed775fbf (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
\begin{filecontents}{byrne-latex.bib}
@book{Byrne1847,
  author = {Byrne, Oliver},
  publisher = {William Pickering},
  title = {{The first six books of the elements of Euclid, in which coloured diagrams and symbols are used instead of letters for the greater ease of learners}},
  year = 1847
}
@book{Tufte90,
  author = {Tufte, Edward R.},
  isbn = {978-0-9613921-1-6},
  publisher = {Graphics Press},
  title = {{Envisioning Information}},
  year = 1990
}
@misc{Slyusarev2017,
  author = {Slyusarev, Sergey},
  title = {{MetaPost + ConTeXt rendition of Oliver Byrne's "The first six books of the Elements of Euclid"}},
  year = {2017},
  howpublished = {\url{https://github.com/jemmybutton/byrne-euclid}}
}
@misc{Rougeux2018,
  author = {Rougeux, Nicholas},
  title = {{Byrne’s Euclid}},
  year = {2018},
  howpublished = {\url{https://www.c82.net/euclid/}}
}
@misc{Okabe2008,
  author = {Okabe, Masataka and Ito, Kei},
  title = {{Color Universal Design (CUD) How to make figures and presentations that are friendly to Colorblind people}},
  year = {2008},
  howpublished = {\url{https://jfly.uni-koeln.de/color/}}
}
\end{filecontents}

\documentclass{ltxdoc}
\usepackage{byrne}
\usepackage{ccicons,bxtexlogo,listings,hyperref}
\hypersetup{
     colorlinks=true,
     linkcolor=blue,
     filecolor=blue,
     citecolor = black,      
     urlcolor=cyan,
     }

\lstset{
language=MetaPost,
alsolanguage=TeX,
numbers=none,
basicstyle=\ttfamily\scriptsize
}

\def\mpPre{textLabels := true;}

\author{Sergey Slyusarev}
\title{``Byrne'' v. 0.2.2 package for \METAPOST\ and \LaTeX}

\begin{document}
\maketitle

\begin{abstract}
This document describes ``Byrne'' package for \METAPOST\ and \LaTeX.
\end{abstract}

\begin{centering}

This document is distributed under CC-BY-SA 4.0 license 

\ccbysa 

\href{https://github.com/jemmybutton/byrne-latex}{https://github.com/jemmybutton/byrne-latex}

\end{centering}

\section{Introduction}
Oliver Byrne's \href{https://archive.org/details/firstsixbooksofe00byrn/}{1847 quirky edition on the first six books of Euclid's ``Elements''}\cite{Byrne1847} is an interesting example of tight interplay between text and graphics in information visualization. The main feature of this book is that instead of relying on letter designations to describe lines, angles, etc., all the diagrams in it are colored and parts of these diagrams are directly incorporated into text.

Recently this work met somewhat of a renaissance and in the span of a couple of years at least three independent attempts were made at reviving Byrne's work. In early 2017 the first six books \href{https://github.com/jemmybutton/byrne-euclid/}{remade in \ConTeXt} were published on GitHub\cite{Slyusarev2017}, in late 2018 an \href{https://www.c82.net/euclid/}{interactive web-version} was published by Nicholas Rougeux\cite{Rougeux2018} and in late 2019 a \href{https://www.kroneckerwallis.com/product/euclids-elements-completing-oliver-byrnes-work/}{printed version} of all Euclid's 15 books was published by Kronecker Wallis. All three are very different in terms of approach and goals.

The \ConTeXt\ version's main objective was to develop a toolkit for applying Byrne's approach to a variety of geometry problems in the least time-consuming manner. This package is a \LaTeX\ (specifically \LuaLaTeX) version of the toolkit. It consists of two parts: \METAPOST\ code to describe and render geometric constructions and \LaTeX\ code to incorporate these constructions in text.

\section{Requirements}

This package works with \LuaLaTeX\ and requires \texttt{luamplib v2.23.0} or higher.
\section{Example}

\begin{minipage}{\textwidth}
\vskip 0.5\baselineskip
\defineNewPicture{
textLabels := true;
angleSize := 1cm;
pair A, B, C;
A := (0, 0);
B := (0, 2cm);
C := (3cm, 0);
byAngleDefine(C, B, A, byyellow, 0);
byAngleDefine(B, A, C, byblue, 0);
byAngleDefine(A, C, B, byred, 0);
draw byNamedAngleResized();
byLineDefine(A, B, byred, 0, 0);    
byLineDefine(B, C, byblue, 0, 0);   
byLineDefine(C, A, byyellow, 0, 0); 
draw byNamedLineSeq(0)(AB,BC,CA);
draw byLabelsOnPolygon(A, B, C)(0, 0);
}
~\hfill\drawCurrentPicture\hfill~
\vskip \baselineskip

In 
\drawFromCurrentPicture[middle][triangleABC]{
startAutoLabeling;
draw byNamedLineSeq(0)(AB,BC,CA);
stopAutoLabeling;
} 
the angle \drawAngle{A} 
is a right angle, therefore \triangleABC 
is a right-angled triangle. 
In it $\drawUnitLine{CB} > \drawUnitLine{AB}$ 
and $\drawUnitLine{BC} > \drawUnitLine{AC}$.
\end{minipage}

\vskip 2\baselineskip
The construction above is described like this:
\vskip 1.5\baselineskip

\begin{lstlisting}
\usepackage{byrne}
...
\defineNewPicture{ % MetaPost code to describe the main diagram is placed inside
  textLabels := true; % This turns text labels on
  pair A, B, C; 
  A := (0, 0);  
  B := (0, 2cm);
  C := (3cm, 0);
  byAngleDefine(C, B, A, byyellow, 0); % This defines a yellow angle CBA
  byAngleDefine(B, A, C, byblue, 0);   
  byAngleDefine(A, C, B, byred, 0);    
  draw byNamedAngleResized(); % Draws angles. 
  byLineDefine(A, B, byred, 0, 0);    % This defines a red line AB. 
  byLineDefine(B, C, byblue, 0, 0);   
  byLineDefine(C, A, byyellow, 0, 0); 
  draw byNamedLineSeq(1)(AB,BC,CA); % Draws joint lines in sequence
  draw byLabelsOnPolygon(A, B, C)(0, 0); % Draws text labels
}                                   
\drawCurrentPicture % Draws the diagram

In 
\drawFromCurrentPicture[middle][triangleABC]{ 
  startAutoLabeling;
  draw byNamedLineSeq(0)(AB,BC,CA);           
  stopAutoLabeling;
}
the angle \drawAngle{A} is a right angle, therefore \triangleABC\ is
a right-angled triangle. In it $\drawUnitLine{CB} > \drawUnitLine{AB}$ 
and $\drawUnitLine{BC} > \drawUnitLine{AC}$. 
\end{lstlisting}

\vskip 1.5\baselineskip

Several things to note here. 

In the \METAPOST\ part: 
All points are ordinary \METAPOST\ pairs and can be defined and manipulated as such. Normally every part of the diagram is first defined (e.g. \texttt{byAngleDefine} or \texttt{byLineDefine}) and then is drawn (e.g. \texttt{draw byNamedAngleResized...} or \texttt{draw byNamedLineSeq...}). Also, although Byrne didn't use text labels in his book, they are implemented in this package \ref{textlabels}. Normally they are placed semi-manually in the main diagram (using functions like \texttt{byLabelsOnPolygon}) and mostly automatically in offspring pictures. By default they are turned off, and to turn them on \texttt{textLabels := true;} should be set.

In the \LaTeX\ part: 
The most general way to reference main diagram is to use \cs{drawFromCurrentPicture}. It will process arbitrary \METAPOST\ code based on the main diagram's code and output an image. However, it would be too cumbersome to use this route every time, so a few shortcuts are in place. If you do need to process arbitrary code, you can give picture a name (in the example it's \texttt{triangleABC}). It will define a macro of the same name \cs{triangleABC} which will output the same image again. For most common cases there are special macros which don't require you to write any \METAPOST\ code. For instance \cs{drawAngle} and \cs{drawUnitLine} allow you to call angles and lines simply by name. The names don't have to match the initial definition exactly. For instance, the angle in the example can be called \texttt{A}, \texttt{BAC} or \texttt{ABC} interchangeably, or the same line segment can be called either \texttt{BC} or \texttt{CB}.

For more examples you can look at the source code of the \href{https://github.com/jemmybutton/byrne-euclid/}{\ConTeXt\ version of Byrne's book.} This package shares syntax with it and its code can be transferred to \LaTeX\ with minimal changes.

The following reference guide is not complete and will be updated in the future.

\section{\METAPOST\ part reference}

\subsection{Global variables and settings}

\subsubsection{Global variables}\label{Variables}
	
	There are several variables which control the looks and behaviour.
	
	\texttt{lineWidth}\label{lineWidth}~— the width for regular lines, set to \texttt{2pt} by default. Normally referenced as \texttt{0}.
	
	\texttt{lineWidthThin}~— the width for thin lines, set to \texttt{1pt} by default. Normally referenced as \texttt{1}.
	
	\texttt{lineWidthHair}~— the width for superthin lines, set to \texttt{1/2pt} by default. Normally referenced as \texttt{2}.
	
	\texttt{pointMarkSize}\label{pointMarkSize}~— size of point marks, set to \texttt{4pt} by default.
	
	\texttt{pointLinesSize}\label{pointLinesSize}~— size for line segments used to depict points, set to \texttt{1/2cm} by default.

	\texttt{defaultScaleFactor}~— global default scale factor, set to \texttt{1} by default.

	\texttt{angleSize}\label{angleSize}~— angle arc radius, set to \texttt{1cm} by default.
	
	\texttt{angleScale}\label{angleScale}~— scale factor for angle arcs, set to \texttt{1} by default.

	\texttt{globalRotation}~— angle to rotate the whole picture.

	\texttt{markLength}~— size of marks on lines, set to \texttt{3lineWidth} by default.

	\texttt{rayExtension}~— length for a ray depiction, set to \texttt{1/3cm} by default.

%	magnitudeSize := 5/18cm;
%	magnitudeScale := 1;
%	magnitudeGap := 3/2lineWidth;
	
	\texttt{textLabels}~— whether to render text labels, set to \texttt{false} by default.

%ghostLines := true;

	\texttt{autoRightAngles}\label{autoRightAngles}~— whether to depict right angles using angles instead of arcs, set to \texttt{false} by default.

%omitDuplicateTextLabels := false;
	
	\texttt{textLabelShift}~— how far away to put text labels from points, set to \texttt{lineWidth} by default.
	
%autoLabelingMode := false;
%mainPictureMode := false;

%pathToString

\subsubsection{defineColor.ColorName(color)}\label{defineColor}
	
	\defineNewPicture{
	textLabels := false;
	pair A, B, C;
	A := dir(60);
	B := (0, 0);
	C := dir(0);
	forsuffixes s=byblack,byred,byblue,byyellow,oiBlack,oiOrange,oiSkyBlue,oiGreen,oiYellow,oiBlue,oiVermillion,oiPurple:
		byAngleDefine.s(A, B, C,s, 0);
	endfor;
	}
	Defines a color. Colors can be defined as regular \METAPOST\ colors as well, this is just a shorthand version.

	\texttt{ColorName}~— mandatory color name of \texttt{suffix type}.
	
	\texttt{color}~— an actual calor, can be either of \texttt{color} type or of \texttt{cmykcolor} type.
	
	Some colors are predefined. Colors similar to the ones Byrne used for his book are: \texttt{byblack}\drawAngle{byblack}, \texttt{byred}\drawAngle{byred}, \texttt{byblue}\drawAngle{byblue}, \texttt{byyellow}\drawAngle{byyellow}. One obvious issue of any color coding is whether the colors are discernible by colorblind people. Byrne's colors should be mostly fine, but there are only foru of them. In case more colors are necessary, eight colors from \href{https://jfly.uni-koeln.de/color/}{colorblind-friendly palette by Okabe and Ito} \cite{Okabe2008} are defined: \texttt{oiBlack}\drawAngle{oiBlack}, \texttt{oiOrange}\drawAngle{oiOrange}, \texttt{oiSkyBlue}\drawAngle{oiSkyBlue}, \texttt{oiGreen}\drawAngle{oiGreen}, \texttt{oiYellow}\drawAngle{oiYellow}, \texttt{oiBlue}\drawAngle{oiBlue}, \texttt{oiVermillion}\drawAngle{oiVermillion}, \texttt{oiPurple}\drawAngle{oiPurple}. Also text labels \ref{textlabels} are helpful as a secondary means of identification.

%\subsubsection{selectOutlineColor.ColorName}\label{selectOutlineColor}
	
%	Selects an outline color for a color.

%	\texttt{ColorName}~— mandatory color name of \texttt{suffix type}.
	
% ...

\subsubsection{startTempScale(tmpScale); ... \METAPOST\ code ... stopTempScale;}\label{startTempScale}

	Used to temporarily set scale factor for a section of code;

	\texttt{tmpScale}~— scale factor for a section of code.
		
\subsubsection{startTempAngleScale(tmpAngleScale); ... \METAPOST\ code ... stopTempAngleScale;}\label{startTempAngleScale}

	Used to temporarily set angle scale factor for a section of code;

	\texttt{tmpAngleScale}~— angle scale factor for a section of code.

\subsubsection{startGlobalRotation(rotationAngle); ... \METAPOST\ code ... stopGlobalRotation;}\label{startGlobalRotation}

	Used to temporarily set global rotation for a section of code;

	\texttt{rotationAngle}~— global rotation for a section of code.
	
\subsubsection{startAutoLabeling; ... \METAPOST\ code ... stopAutoLabeling}\label{startAutoLabeling}

	Used to turn auto labeling for a section of code. Most of the drawing functions have auto labeling which is turned off by default. Sometimes it's handy to use it instead of labeling items by hand.

%startOffspringPictureMode
%stopOffspringPictureMode

%startMainPictureMode
%stopMainPictureMode

\subsection{Lines}

% byLineRender
% byReturnLineLength

\subsubsection{byLineDefine.LineName(A, B, color, dashed, thick)}\label{byLineDefine}

	Defines a straight line. Does not return anything.
	
	\texttt{LineName}~— optional line name of \texttt{suffix type}. If no name is provided, it is being constructed from point names, e.g. \texttt{AB}.
	
	\texttt{A, B}~— point names, of \texttt{suffix} type (i.e., variable names should be provided).
	
	\texttt{color}~— line color, of \texttt{color} type.
	
	\texttt{dashed}~— is line dashed. \texttt{0} for solid line and \texttt{1} for dashed line.
	
	\texttt{thick}~— is line thick. \texttt{0} for regular line and \texttt{1} for thin line \ref{lineWidth}.

	\defineNewPicture{
		pair A, B, C, D;
		A := (0, 0);
		B := (2cm, 0);
		C := (3cm, 0);
		D := (5cm, 0);
		byLineDefine(A, B, byred, 0, 0);
		byLineDefine(C, D, byblue, 1, 1);
	}
	For example, this line \drawUnitLine{AB} is defined as \texttt{byLineDefine(A, B, byred, 0, 0);} and this line \drawUnitLine{CD} is defined as \texttt{byLineDefine(C, D, byblue, 1, 1);}

% byLineStylize

\subsubsection{byLine.LineName(A, B, color, dashed, thick)}\label{byLine}

	Defines and draws a straight line. Returns a \texttt{picture} of the line.
	
	Arguments are the same as in \texttt{byLineDefine} \ref{byLineDefine}.

% byLineFull
% byLineWithName
% byNamedLineFull

\subsubsection{byNamedLine(LINES\_LIST)}\label{byNamedLine}

	Draws lines. Returns a picture of the lines.
	
	\texttt{LINES\_LIST}~— a comma-separated list of line names.

\subsubsection{byNamedLineSeq(lineShift)(LINES\_LIST)}\label{byNamedLineSeq}

	\defineNewPicture[1]{
		pair A, B, C;
		A :=  dir(45) scaled 1/4cm;
		B := (0, 0);
		C :=  dir(0) scaled 1/4cm;
		byLineDefine(A, B, byred, 0, 0);
		byLineDefine(B,C, byyellow, 0, 0);
		draw byNamedLineSeq(0)(BC,AB) scaled 2;
	}
		
	Draws lines joined in sequence. Line joints look like this:\drawCurrentPicture. Returns a picture of the lines.
	
	\texttt{lineShift}~— how much the lines are shifted perpendicular lines' axis. \texttt{1} is for one regular line thickness to one side%
	\drawFromCurrentPicture[bottom]{
	draw byNamedLineSeq(1)(BC,AB) scaled 2;
	draw (A--B--C) scaled 2 withpen pencircle scaled 1/2pt;
	}, 
	\texttt{-1} is for one regular line thickness to the other side%
	\drawFromCurrentPicture[bottom]{
		draw byNamedLineSeq(-1)(BC,AB) scaled 2;
		draw (A--B--C) scaled 2 withpen pencircle scaled 1/2pt;
	}.
	
	\texttt{LINES\_LIST}~— a comma-separated list of line names.
	

\subsubsection{byMarkLine(position, color)(LineName)}\label{byMarkLine}

	\defineNewPicture[1]{
		pair A, B;
		A := (0, 0);
		B := (1cm, 0);
		byLineDefine(A, B, byblue, 0, 0);
	}
	
	Defines and draws a mark on a line.
	
	\texttt{position}~— a position of the mark. \texttt{0} for one end of the line, \texttt{1} for the other end of the line.
	
	\texttt{color}~— mark color, of \texttt{color} type.
	
	\texttt{LineName}~— line name, of \texttt{suffix} type.
	
	For example this line mark \drawFromCurrentPicture{
		startAutoLabeling;
		draw byNamedLine(AB);
		draw byLabelLine(0)(AB);
		draw byMarkLine(1/4, byred, AB);
		stopAutoLabeling;
	} is drawn with \texttt{draw byMarkLine(1/4, byred, AB);}.

\subsubsection{byNamedMarkLine(LineName)}

	Draws a defined mark on the given line.
	
	\texttt{LineName}~— line name, of \texttt{suffix} type.
	
%byFindLinePointedThere
%byConstructCompoundLine
%byExpandLines
%byNamedCompoundLine
%byNamedCompoundRay
%byNamedCompoundIndLine
%byNamedCompoundLineRender
%generateLineSynonyms

\subsection{Points}

\subsubsection{byPointLabelDefine(A, pointLabel)}\label{byPointLabelDefine}

	Defines a point text label, returns nothing. By default point names are the same as the names of respective variables.
	
	\texttt{A}~— a name of a point of \texttt{suffix} type  (i.e., variable name should be provided).
	
	\texttt{pointLabel}~— point label of \texttt{string} type.

\subsubsection{byPointLabelRemove(POINTS\_LIST)}\label{byPointLabelRemove}

	Sets text labels of multiple points to blank. Useful if text labels are turned on, but you don't want labels on certain points.

	\texttt{POINTS\_LIST}~— a comma-separated list of point names.

\subsubsection{byPointMarkDefine(PointName)(color, style)}\label{byPointMarkDefine}

	\defineNewPicture{
		textLabels := false;
		pair A, B;
		A := (0, 0);
		B := (1cm, 0);
		draw byPointMark(A,  byblue, 0);
		draw byPointMark(B,  byred, 1);
	}
	
	Defines a point mark.

	\texttt{color}~— mark color, of \texttt{color} type.

	\texttt{style}~— \texttt{0} for solid circle \drawPointM{A}, \texttt{1} for white circle with outline \drawPointM{B}. Mark size is controlled by \texttt{pointMarkSize} \ref{pointMarkSize}.
		
%byPointXYZDefine
%byPointXYZEmpty
%byIsPointInSpace
%byPair
%byRotatePoints
%byPointMarkRender
%byNamedPointMark
%byPointMark
%byNamedPointLines

\subsection{Arcs and circles}

%byCirclePathGenerate
%byArcRender

\subsubsection{byArcDefineBE.ArcName(O, begin, end, radius, color, dashed, thick, shift, endType)}\label{byArcDefineBE}

	Defines an arc based on its center, radius and two angles. Returns nothing.

	\defineNewPicture[1]{
		textLabels := false;
		pair A, B;
		A := (0, 0);
	}
	
	\texttt{ArcName}~— optional arc name of \texttt{suffix type}. If no name is provided, it is being constructed from center point name, e.g. \texttt{O}.
	
	\texttt{O}~— the center of the circle an arc is from, of \texttt{suffix} type (i.e., variable name should be provided).
	
	\texttt{begin, end}~— beginning and ending of the arc in eighths (in essence, \texttt{arctime} of \texttt{fullcircle}). \texttt{0} for 3 o'clock, \texttt{2} for 12 o'clock etc. For instance, this
	\drawFromCurrentPicture{
		draw byArcBE(A, 0, 3, 2/6cm, byblue, 0, 0, 1, 0);
	}
	is \texttt{0, 3} and this
	\drawFromCurrentPicture{
		draw byArcBE(A, 5, 7, 2/6cm, byblue, 0, 0, 1, 0);
	}	
	is \texttt{5, 7}.
	
	\texttt{radius}~— arc radius.
	
	\texttt{color}~— arc color, of \texttt{color} type.
	
	\texttt{dashed}~— is arc line dashed. \texttt{0} for solid line and \texttt{1} for dashed line.
	
	\texttt{thick}~— is arc line thick. \texttt{0} for regular line and \texttt{1} for thin line \ref{lineWidth}.
	
	\texttt{shift}~— how much arc line is shifted. \texttt{1} is for one regular line thickness outwards
	\drawFromCurrentPicture{
		draw byArcBE(A, 1/2, 7/2, 1/6cm, byyellow, 0, 0, 1, 0) scaled 2;
		draw (subpath (1/2, 7/2) of (fullcircle scaled 4/6cm)) withpen pencircle scaled 1/2pt;
	}, \texttt{-1} is for one regular line thickness inwards
	\drawFromCurrentPicture{
		draw byArcBE(A, 1/2, 7/2, 1/6cm, byyellow, 0, 0, -1, 0) scaled 2;
		draw (subpath (1/2, 7/2) of (fullcircle scaled 4/6cm)) withpen pencircle scaled 1/2pt;
	}.
	
	\texttt{endType}~— type of arc line ends. \texttt{0} for ends cut by the radii
	\drawFromCurrentPicture{
		draw byArcBE(A, 1/2, 7/2, 1/6cm, byred, 0, 0, 0, 0) scaled 2;
	}
	and \texttt{1} for ends cut by the chord
	\drawFromCurrentPicture{
		draw byArcBE(A, 1/2, 7/2, 1/6cm, byred, 0, 0, 0, 1) scaled 2;
	}.

\subsubsection{byArcBE.arcName(O, begin, end, radius, color, dashed, thick, shift, endType)}\label{byArcBE}

	Defines and draws an arc based on its center, radius and two angles. Returns the picture of the arc.
	
	Arguments are the same as in \texttt{byArcDefineBE} \ref{byArcDefineBE}.

\subsubsection{byArcDefine.ArcName(O, B, E, radius, color, dashed, thick, shift, endType)}\label{byArcDefine}
	
	Defines an arc based on its center, radius and two points. Returns nothing.
	
	Arguments are the same as in \texttt{byArcDefineBE} \ref{byArcDefineBE}, except for instead of angles in eights points are used.
	
	\texttt{ArcName}~— optional arc name of \texttt{suffix type}. If no name is provided, it is being constructed from point names, e.g. \texttt{BOE}.
	
	\texttt{B, E}~— points in the direction of the beginning and the ending of the arc respectively. Of \texttt{suffix} type (i.e., variable names should be provided).

\subsubsection{byArc.ArcName(O, B, E, radius, color, dashed, thick, shift, endType))}\label{byArc}
	
	Arguments are the same as in \texttt{byArcDefine} \ref{byArcDefine}.
	
\subsubsection{byNamedArcExact(ARCS\_LIST)}\label{byNamedArcExact}
	Draws a picture of arcs just as they were defined. Returns a picture of the arcs.
	
	\texttt{ARCS\_LIST}~— a comma-separated list of arc names.
	
\subsubsection{byNamedArc(ARCS\_LIST)}\label{byNamedArc}
	Draws a picture of arcs, except of it ignores \texttt{shift} and \texttt{endType}. Returns a picture of the arcs.
	
	\texttt{ARCS\_LIST}~— a comma-separated list of arc names.

%byNamedArcLabel

\subsubsection{byCircleDefineFree.CircleName(o, radius, color, dashed, thick, shift)}\label{byCircleDefineFree}
	
	Defines a circle based on its center and radius. Returns nothing.
	
	\defineNewPicture[1]{
	}
	
	\texttt{CircleName}~— optional circle name of \texttt{suffix type}. If no name is provided, \texttt{aCircle} is used for a name.
	
	\texttt{o}~— the center of the circle, of \texttt{pair} type.
	
	\texttt{radius}~— circle radius.
	
	\texttt{color}~— circle color, of \texttt{color} type.
	
	\texttt{dashed}~— is circle line dashed. \texttt{0} for solid line and \texttt{1} for dashed line.
	
	\texttt{thick}~— is circle line thick. \texttt{0} for regular line and \texttt{1} for thin line \ref{lineWidth}.
	
	\texttt{shift}~— how much circle line is shifted. \texttt{1} is for one regular line thickness outwards
	\drawFromCurrentPicture{
		byCircleDefineFree((0,0), 1/8cm, byyellow, 0, 0, 1);
		draw byNamedCircle(aCircle) scaled 2;
		draw fullcircle scaled 1/2cm;
	}, \texttt{-1} is for one regular line thickness inwards
	\drawFromCurrentPicture{
		byCircleDefineFree((0,0), 1/8cm, byyellow, 0, 0, -1);
		draw byNamedCircle(aCircle) scaled 2;
		draw fullcircle scaled 1/2cm;
	}.

\subsubsection{byCircleDefineR.CircleName(O, radius, color, dashed, thick, shift)}\label{byCircleDefineR}
	
	Defines a circle based on its center and radius. Returns nothing.
	
	Arguments are the same as in \texttt{byCircleDefineFree} \ref{byCircleDefineFree}, except for the center is not defined directly by a \texttt{pair}.
	
	\texttt{CircleName}~— optional circle name of \texttt{suffix type}. If no name is provided, it is being constructed from center name, e.g. \texttt{O}.
	
	\texttt{O}~— the center of the circle. Of \texttt{suffix} type (i.e., variable name should be provided).

\subsubsection{byCircleR.CircleName(O, radius, color, dashed, thick, shift)}\label{byCircleR}
	
	Defines and draws circle based on its center and radius. Returns a picture of that circle.
	
	Arguments are the same as in \texttt{byCircleDefineR} \ref{byCircleDefineR}.

\subsubsection{byCircleDefine.CircleName(O, A, color, dashed, thick, shift)}\label{byCircleDefine}
	
	Defines circle based on its center and a point. Returns nothing.
	
	Arguments are the same as in \texttt{byCircleDefineR} \ref{byCircleDefineR}, except for instead of the radius, a point through which the circle is drawn is used.
	
	\texttt{CircleName}~— optional circle name of \texttt{suffix type}. If no name is provided, it is being constructed from point names, e.g. \texttt{OA}.
	
	\texttt{A}~— a point through which the circle is drawn. Of \texttt{suffix} type (i.e., variable name should be provided).

\subsubsection{byCircle.CircleName(O, A, color, dashed, thick, shift)}\label{byCircle}
	
	Defines and draws circle based on its center and a point. Returns a picture of that circle.
	
	Arguments are the same as in \texttt{byCircleDefine} \ref{byCircleDefine}.

\subsubsection{byCircleABC.CircleName(A, B, C, color, dashed, thick, shift)}\label{byCircleABC}
	
	Arguments are the same as in \texttt{byCircleDefineR} \ref{byCircleDefineR}, except for instead of the center and the radius, three points through which the circle is drawn are used.
	
	\texttt{CircleName}~— optional circle name of \texttt{suffix type}. If no name is provided, it is being constructed from point names, e.g. \texttt{ABC}.
	
	\texttt{A, B, C}~— points through which the circle is drawn. Of \texttt{suffix} type (i.e., variable names should be provided).

%byFindCircleCenterABC
%byFindCircleCenterABCinSpace
%byReturnCircleCenter

\subsubsection{byNamedCircle(CIRCLES\_LIST)}\label{byNamedCircle}
	
	Draws circles. Returns a picture of the circles.
	
	\texttt{CIRCLES\_LIST}~— a comma-separated list of circle names.

\subsection{Arbitraty figures}

\subsubsection{byArbitraryFigureDefine.ArbitraryFigureName(figurePath, col\-or, dashed, thick)}\label{byArbitraryFigureDefine}
	
	Defines an arbitrary figure (basically, any path). Returns nothing.
	
	\texttt{ArbitraryFigureName}~— optional figure name of \texttt{suffix type}. If no name is provided, \texttt{anArbitraryFigure} is used for a name.
	
	\texttt{figurePath}~— figure path, of \texttt{path} type.
	
	\texttt{color}~— figure color, of \texttt{color} type.
	
	\texttt{dashed}~— is figure line dashed. \texttt{0} for solid line and \texttt{1} for dashed line.
	
	\texttt{thick}~— is figure line thick. \texttt{0} for regular line and \texttt{1} for thin line \ref{lineWidth}.

\subsubsection{byArbitraryFigure.ArbitraryFigureName(figurePath, color, dash\-ed, thick)}\label{byArbitraryFigure}

	Defines an arbitrary figure. Returns nothing.
	
	Arguments are the same as in \texttt{byArbitraryFigure} \ref{byArbitraryFigure}.

\subsubsection{byNamedArbitraryFigure(ARBITRARY\_FIGURES\_LIST)}\label{byNamedArbitraryFigure}

	Draws arbitrary figures. Returns a picture of the figures.
	
	\texttt{ARBITRARY\_FIGURES\_LIST}~— a comma-separated list of figure names.

%byArbitraryFigureRender
%byArbitraryCurveDefine
%byNamedArbitraryCurve
%byListToPath
%byArbitraryCurve

\subsection{Filled figures}

%byFilledCircleSegment
%byNamedFilledCircleSegment
%byFilledCircleSector
%byNamedFilledCircleSector

\subsubsection{byPolygonDefine.PolygonName(POINTS\_LIST)(Color)}\label{byPolygonDefine}

	Defines a polygon based on its vertex points. Returns nothing.
	
	\texttt{PolygonName}~— optional polygon name \texttt{suffix}.
	
	\texttt{POINTS\_LIST}~— a comma-separated list of point names.
	
	\texttt{Color}~— line color, of \texttt{suffix} type (i.e. a variable name should be provided).

%byPolygonPathFromList

\subsubsection{byPolygon.polygonName(POINTS\_LIST)(Color)}\label{byPolygon}

	Defines and draws a polygon based on its vertex points. Returns a picture of the polygon.
	
	Arguments are the same as in \texttt{byPolygonDefine} \ref{byPolygonDefine}.

%byPolygonName

\subsubsection{byNamedPolygon(POLYGONS\_LIST)}\label{byNamedPolygon}
	
	Draws polygons. Returns a picture of the polygons.
	
	\texttt{POLYGONS\_LIST}~— a comma-separated list of polygon names.

%byMergePolygons
%polygonCleanup

\subsection{Angles}

\subsubsection{byAngleDefine.AngleName(A, B, C, color, style)}\label{byAngleDefine}
	
	\defineNewPicture{
		textLabels := false;
		pair A, B, C, A', B', C', A'', B'', C'';
		A :=  dir(60);
		B := (0, 0);
		C :=  dir(0);
		A' := A shifted (1cm, 0);
		B' := B shifted (1cm, 0);
		C' := C shifted (1cm, 0);
		A'' := A shifted (2cm, 0);
		B'' := B shifted (2cm, 0);
		C'' := C shifted (2cm, 0);
		byAngleDefine(A, B, C, byred, 0);
		byAngleDefine(A', B', C', byred, 1);
		byAngleDefine(A'', B'', C'', byred, 2);
	}
	
	Defines an angle based on three points. Returns nothing.

	\texttt{AngleName}~— optional angle name \texttt{suffix}.
		
	\texttt{A, B, C}~— angle points. Of \texttt{suffix} type (i.e., variable names should be provided).
	
	\texttt{color}~— angle color, of \texttt{color} type.
	
	\texttt{style}~— angle arc style. \texttt{0} for solid filled sector \drawAngle{B}, \texttt{1} for arc \drawAngle{B'}, \texttt{2} for dashed arc \drawAngle{B''}. Default arc radius is determined by \texttt{angleSize} \ref{angleSize}. It can be temporarily changed using \texttt{angleScale} \ref{angleScale}. You can also define custom angle styles \ref{AngleStyles}. 
	
\subsubsection{byConsiderAngleRight(AngleName)}\label{byConsiderAngleRight}

	\defineNewPicture{
	textLabels := false;
	pair A, B, C, A', B', C';
	A := dir(60)*cm;
	B := (0, 0);
	C := dir(0)*cm;
	A' := A shifted (2cm, 0);
	B' := B shifted (2cm, 0);
	C' := C shifted (2cm, 0);
	byAngleDefine(A, B, C, byyellow, 0);
	byAngleDefine(A', B', C', byyellow, 0);
	byConsiderAngleRight(A'B'C');
	}
	Makes a defined angle look like an angle \drawAngle{A'B'C'} instead of a circle arc \drawAngle{ABC}, as right angles are often depicted. Useful if an angle is not actually right in the diagram, but is meant to be right or assumed to be right. To make all the right angles look like this automatically, you can set \texttt{autoRightAngles := true;}\ref{autoRightAngles}.
	
	\texttt{AngleName}~— name of the angle. 

%byConstructAngleArc
%byIsArcClockwise
%byFullCircleToPlane

\subsubsection{byAngle.AngleName(A, B, C, color, style)}\label{byAngle}

	Defines and draws an angle based on three points. Returns a picture of the angle.
	
	Arguments are the same as in \texttt{byAngleDefine} \ref{byAngleDefine}.

\subsubsection{byAngleDefineExtended.AngleName(A, B, C, color, style)(OPTIONAL\_COLORS\_LIST)}\label{byAngleDefineExtended}

	Defines an angle based on three points. Returns nothing.
	
	Arguments are the same as in \texttt{byAngleDefine} \ref{byAngleDefine}, except for using this function it's possible to define optional colors for an angle.
	
	\texttt{OPTIONAL\_COLORS\_LIST}~— a comma-separated list of optional color names. See \ref{AngleStyles} for details.
	
\subsubsection{byAngleExtended.AngleName(A, B, C, color, style)(OPTION\-AL\_COLORS\_LIST)}\label{byAngleExtended}

	Defines and draws an angle based on three points. Returns a picture of the angle.
	
	Arguments are the same as in \texttt{byAngleDefineExtended} \ref{byAngleDefineExtended}.

\subsubsection{byNamedAngle(ANGLES\_LIST)}\label{byNamedAngle}
	
	Draws angles. Returns a picture of the angles.
	
	\texttt{ANGLES\_LIST}~— a comma-separated list of polygon names.

%byNamedSolidAngle
%byProcessAnglesList
%byAngleMWhite
%byAngleMSolid
%byAngleMLine
%byAngleMThinLine
%byAngleMDashedLine
%byNamedAngleSidesFull
%byNamedAngleDummySides
%byNamedAngleSides
%byNamedAngleWithDummySides
%byNamedAngleResized
%generateAngleSynonyms
%sortPointAnglesList
%bySplitStringIntoAngles
%byConstructCompoundAngle
%twoRightAngles
%rightAngle
%byDefineGenericRightAngles

\subsubsection{Angle styles}\label{AngleStyles}

	It's possible to add custom angle styles. To do this, you first need to define a function, with a particular set of arguments and then include this function's name into a special list. As an example here's the function which describes a regular solid angle sector:
	
\begin{lstlisting}
vardef byAngleMSolid (expr angleArc, angleColor)(suffix AngleOptionalColors) =
    save p;
    path p;
    p := angleArc scaled (angleScale*angleSize);
    image(
        fill ((0, 0)--p--cycle) withcolor angleColor;
    )
enddef;
\end{lstlisting}

	Note the argument \texttt{AngleOptionalColors}. It is not used for solid angles and is not defined with \texttt{byAngleDefine}, but several optional colors can be defined using \texttt{byAngleDefineExtended} \ref{byAngleDefineExtended} and can be accessed using \texttt{AngleOptionalColors[0]}, \texttt{AngleOptionalColors[1]} etc.

	And here's how this angle style is included in the list:

\begin{lstlisting}
byAngleMacroName[0] := "byAngleMSolid";
\end{lstlisting}

	Here \texttt{0} is the value of \texttt{sty} argument used in \texttt{byAngleDefine} \ref{byAngleDefine} and such to call this particular angle style.
	
	As a more practical example, in Byrne's book, in a couple of places for some reason he chooses not to use ordinary arcs and sectors, but instead goes with unique angle designs. In order not to include these peculiarities into the main lib in the \ConTeXt\ version they were defined \textit{in situ}. Here's the definition from IV.III:

	\defineNewPicture{
		vardef byAngleMSectors (expr angleArc, angleColor)(suffix angleOptionalColors) =
		    save p;
		    path p[];
		    p1 := (subpath(0, arctime (1/3arclength(angleArc)) of angleArc) 
		    	of angleArc) 
		    	scaled (angleScale*angleSize);
		    p2 := (subpath(arctime (1/3arclength(angleArc)) 
		    	of angleArc, arctime(2/3arclength(angleArc)) of angleArc) of angleArc) 
		    	scaled (angleScale*angleSize);
		    p3 := (subpath(arctime (2/3arclength(angleArc)) 
		    	of angleArc, length(angleArc)) of angleArc) 
		    	scaled (angleScale*angleSize);
		    image(
		        fill ((0, 0)--p1--cycle) withcolor angleOptionalColors[0];
		        fill ((0, 0)--p2--cycle) withcolor angleColor;
		        fill ((0, 0)--p3--cycle) withcolor angleOptionalColors[1];
		    )
		enddef;
		byAngleMacroName[3] := "byAngleMSectors";
		textLabels := false;
		pair A, B, C;
		A :=  dir(45) scaled 1/4cm;
		B := (0, 0);
		C :=  dir(0) scaled 1/4cm;
		byAngleDefineExtended(A, B, C, byred, 3)(byblue, byyellow);
	}
	
\begin{lstlisting}	
vardef byAngleMSectors (expr angleArc, angleColor)(suffix angleOptionalColors) =
    save p;
    path p[];
    p1 := (subpath(0, arctime (1/3arclength(angleArc)) of angleArc) 
    	of angleArc) 
    	scaled (angleScale*angleSize);
    p2 := (subpath(arctime (1/3arclength(angleArc)) 
    	of angleArc, arctime(2/3arclength(angleArc)) of angleArc) of angleArc) 
    	scaled (angleScale*angleSize);
    p3 := (subpath(arctime (2/3arclength(angleArc)) 
    	of angleArc, length(angleArc)) of angleArc) 
    	scaled (angleScale*angleSize);
    image(
        fill ((0, 0)--p1--cycle) withcolor angleOptionalColors[0];
        fill ((0, 0)--p2--cycle) withcolor angleColor;
        fill ((0, 0)--p3--cycle) withcolor angleOptionalColors[1];
    )
enddef;
byAngleMacroName[3] := "byAngleMSectors";
\end{lstlisting}

This angle style employs two optional colors and can be called by setting \texttt{style} argument \ref{byAngleDefine} to \texttt{3}. This is what the result of \texttt{byAngleDefineExtended(A, B, C, byred, 3)(byblue, byyellow);} (\ref{byAngleDefineExtended}) looks like:\drawAngle{B}.
%https://archive.org/details/firstsixbooksofe00byrn/page/126/mode/2up

%\subsection{Arrows}

%commonArrowSettings
%byRotationArrowDefine
%byGenerateRotationArrowPath
%byNamedRotationArrow
%byFlatArrowDefine
%byNamedFlatArrow

%\subsection{Spheres}

%\subsection{Magnitudes}

%byMagnitudeSymbolDefine
%byNamedMagnitudeSymbol
%byMagnitudeDefine
%byNamedMagnitude

\subsection{Text labels}\label{textlabels}

There are no text labels in Byrne's book, but, as Edward Tufte points out in his 1990 book, adding small text labels can actually help speed recognition of geometric elements \cite{Tufte90}. It's not clear whether it's indeed the case for the reader, but at the very least text labels provide the author with the means of linking source code with the rendered pages. Several functions listed below allow for adding text labels very similar to the ones suggested by Tufte.

Text labels are turned off by default. As a result, simply adding code for text labels won't make them visible. They only appear when \texttt{textLabels := true;} is set in the beginning of a main picture or globally by defining \texttt{\textbackslash def\textbackslash\{...\} mpPre} \ref{defineNewPicture}. Text labels don't always have to be added manually, most elements can do auto labeling \ref{startAutoLabeling} which is intended to work with standalone angles, polygons, etc. 

%\subsubsection{byTextLabel(labelType, text, point, angle, distance)}\label{byTextLabel}
%Draws a text label. Returns a picture of the label.

\subsubsection{byLabelPoint(A, labelAngle, distance)}\label{byLabelPoint}
Draws a text label for a point. Returns a picture of the label.
	
	\texttt{A}~— the point to label, of \texttt{suffix} type (i.e., point name should be provided).
	
	\texttt{labelAngle}~— angle at which the label should be drawn in degrees.
	
	\texttt{distance}~— distance at which the label should be drawn in \texttt{textLabelShift} units.

\subsubsection{byLabelLine(distance)(LINES\_LIST)}\label{byLabelLine}
	
	Draws text labels for lines. Returns a picture of the labels.
	
	\texttt{distance}~— distance at which the labels should be drawn in \texttt{textLabelShift} units.
	
	\texttt{LINES\_LIST}~— a comma-separated list of line names.

\subsubsection{byLabelPolygon(distance)(POLYGONS\_LIST)}\label{byLabelPolygon}
	
	Draws text labels for polygons. Returns a picture of the labels.
	
	\texttt{distance}~— distance at which the labels should be drawn in \texttt{textLabelShift} units.
	
	\texttt{POLYGONS\_LIST}~— a comma-separated list of polygon names.

%byLabelCircle

\subsubsection{byLabelsOnCircle(POINTS\_LIST)(CircleName)}\label{byLabelsOnCircle}
	
	Draws text labels for points on a circle. Returns a picture of the labels.
	
	\texttt{POINTS\_LIST}~— a comma-separated list of point names.
	
	\texttt{CircleName}~— circle name of \texttt{suffix type}.

\subsubsection{byLabelsOnPolygon(POINTS\_LIST)(style, shift)}\label{byLabelsOnPolygon}
	
	Draws text labels for points on a polygon. Returns a picture of the labels.
	
	\defineNewPicture{
	pair A, B, C, D;
	D := (0, 0);
	C := (1cm, 0);
	B := (2cm, 0);
	A := (1/2cm, 1cm);
	byPolygonDefine(D, C, A)(byred);
	byPolygonDefine(C, B, A)(byyellow);
	}
	
	\texttt{POINTS\_LIST}~— a comma-separated list of point names.
	
	\texttt{style}~— specifies which points to omit. \texttt{0} to draw labels for all listed points
	\drawFromCurrentPicture{
	draw byNamedPolygon(DCA,CBA);
	draw byLabelsOnPolygon(A, B, C, D)(0, 0);
	}, \texttt{1} to draw labels for all listed points, except for the ones at straight angles
	\drawFromCurrentPicture{
	draw byNamedPolygon(DCA,CBA);
	draw byLabelsOnPolygon(A, B, C, D)(1, 0);
	}, \texttt{2} omits first and last points
	\drawFromCurrentPicture{
	draw byNamedPolygon(DCA,CBA);
	draw byLabelsOnPolygon(A, B, C, D)(2, 0);
	}, \texttt{3} omits the first point
	\drawFromCurrentPicture{
	draw byNamedPolygon(DCA,CBA);
	draw byLabelsOnPolygon(A, B, C, D)(3, 0);
	}, \texttt{4} omits the last point
	\drawFromCurrentPicture{
	draw byNamedPolygon(DCA,CBA);
	draw byLabelsOnPolygon(A, B, C, D)(4, 0);
	}.
	
	\texttt{shift}~— negative to move labels closer, positive to move labels farther.

\subsubsection{byLabelLineEnd(A, B)(distance)}\label{byLabelLineEnd}
	
	Draws a text label for a line end. Returns a picture of the label.
	
	\texttt{A, B}~— line ends, of \texttt{suffix} type (i.e., point name should be provided).
	
	\texttt{distance}~— negative to move labels closer, positive to move labels farther.

%byLabelAngleCompensate

\section{\LaTeX\ part reference}

\subsection{General purpose}

\sloppy

\subsubsection{\textbackslash defineNewPicture [offspringPicture\-Sca\-leFactor] [mainPicture\-Sca\-le\-Factor] \{\METAPOST\ code\}}\label{defineNewPicture}

\fussy 

	This macro is used to describe a main diagram.

	\texttt{offspringPictureScaleFactor}~— how much smaller offspring pictures should be. \texttt{1/3} by default.
	
	\texttt{mainPictureScaleFactor}~— scale factor for the main picture. \texttt{1} by default.
	
	\texttt{\METAPOST\ code}~— actual \METAPOST\ code to describe the main picture. To have some snippets of code always executed before and after the code for the main picture (e.g. to turn on text labels by default with \texttt{textLabels := true;}), define \cs{mpPre} and \cs{mpPost} macros respectively in the preamble of your document, like this:
	
\begin{lstlisting}
\def\mpPre{...some \METAPOST\ code...}
\def\mpPost{...some \METAPOST\ code...}
\end{lstlisting}


\subsubsection{\textbackslash drawCurrentPicture}
	
	Draws the main diagram.

% \drawImageFromCurrentInstance

% \unmarkPictAsReady

% \addToUndefineList

\sloppy

\subsubsection{\textbackslash defineFromCurrentPicture \{verticalAlignment\} \{PictureName\} \{\METAPOST\ code\}}

\fussy

	This macro is used to describe a diagram, based on the main diagram.

	\texttt{verticalAlignment}~— vertical alignment declaration. \texttt{middle} to align the picture with the middle of the line, anything else for bottom alignment.

	\texttt{PictureName}~— picture name.

	\texttt{MP code}~— actual \METAPOST\ code to describe the picture.
	
	Can be drawn using \texttt{\textbackslash PictureName}.
	
\sloppy

\subsubsection{\textbackslash drawFromCurrentPicture [verticalAlignment] [PictureName] \{\METAPOST\nolinebreak\ code\}}
 
 \fussy
  
	This macro is used to describe and draw a diagram, based on the main diagram.

	\texttt{verticalAlignment}~— optional vertical alignment declaration. \texttt{middle} to align the picture with the middle of the line, anything else for bottom alignment.

	\texttt{PictureName}~— optional picture name.

	\texttt{\METAPOST\ code}~— actual \METAPOST\ code to describe the picture.
	
	Can be drawn again later using \texttt{\textbackslash PictureName}.

% \drawDefinedPicture

\subsection{Specialized}

\subsubsection{\textbackslash drawUnitLine[LineSecondName]\{LineName\}}

	Draws a line of unit length with colors and labels based on the line of the same name in the main diagram.

	\texttt{LineSecondName}~— optional line name.
	
	\texttt{LineName}~— name of the line to reference in the main diagram. 

	If a name is given, can be called later using \texttt{\textbackslash ulineLineNameLineSecondName}, otherwise~— \texttt{\textbackslash ulineLineName}. 

\subsubsection{\textbackslash drawProportionalLine\{LineName\}}

	Draws a line with colors and labels based on and length linearly proportional to the line of the same name in the main diagram.

	\texttt{LineName}~— name of the line to reference in the main diagram. 
	
	Can be called later using \texttt{\textbackslash plineLineName}.

%\drawProportionalLine

\subsubsection{\textbackslash drawSizedLine[LineSecondName]\{LineName\}}

	Draws a line with colors and labels based on and length proportional to the line of the same name in the main diagram.

	\texttt{LineSecondName}~— optional line name. 
	
	\texttt{LineName}~— name of the line to reference in the main diagram. 
	
	If a name is given, can be called later using \texttt{\textbackslash slineLineNameLineSecondName}, otherwise~— \texttt{\textbackslash slineLineName}. 

\subsubsection{\textbackslash drawUnitRay[RayName]\{LineName\}}

	Draws a ray of unit length with colors and labels based on the line of the same name in the main diagram.

	\texttt{RayName}~— optional ray name.
	
	\texttt{LineName}~— name of the line to reference in the main diagram. 

	If a name is given, can be called later using \texttt{\textbackslash urayLineNameRayName}, otherwise~— \texttt{\textbackslash urayLineName}. 

%\subsubsection{\textbackslash drawProportionalRay\{LineName\}}

%	Draws a ray.

%	\texttt{LineName}~— name of the line to reference in the main diagram. 
	
%	Can be called later using \texttt{\textbackslash prayAngleName}.

%\drawSizedRay

%\drawUnitIndLine

%\drawProportionalIndLine

\subsubsection{\textbackslash drawRightAngle, \textbackslash drawTwoRightAngles}
	\defineNewPicture{textLabels := false;}
	Draws a right angle \drawRightAngle\ and two right angles \drawTwoRightAngles\ respectively. 
	
	More broadly, following generic right angles are defined: \texttt{rightAngleNE} \drawAngle{rightAngleNE},  \texttt{rightAngleES} \drawAngle{rightAngleES},  \texttt{rightAngleSW} \drawAngle{rightAngleSW},  \texttt{rightAngleWN} \drawAngle{rightAngleWN}. 
	
	If you choose to go with angles instead of arcs for right angles (\ref{autoRightAngles}, \ref{byConsiderAngleRight}), adding \texttt{autoRightAngles := true;} to \texttt{\textbackslash mpPre} \ref{defineNewPicture} won't change the appearance of these angles, since they are defined before \texttt{\textbackslash mpPre} commands are executed. Instead, these angles should be redefined. There's a special command for this purpose: \texttt{byDefineGenericRightAngles(true);} where \texttt{true} tells this command to run \texttt{byConsiderAngleRight} \ref{byConsiderAngleRight} for each of the generic right angles.

\subsubsection{\textbackslash drawAngle\{AngleName\}}\label{drawAngle}

	Draws an angle.
	
	\defineNewPicture{
	pair A, B, C, D, E, O;
	O := (0, 0);
	A := (2cm, 0);
	B := A rotated (360/5);
	C := B rotated (360/5);
	D := C rotated (360/5);
	E := D rotated (360/5);
	byAngleDefine(A, O, B, byred, 0);
	byAngleDefine(B, O, C, byyellow, 0);
	byAngleDefine(C, O, D, byblue, 0);
	byAngleDefine(D, O, E, byblack, 0);
	byAngleDefine(E, O, A, byblack, 1);
	byLineDefine(A, O, byblack, 0, 0);
	}

	\texttt{AngleName}~— name of the angle to reference in the main diagram. 
	When just one letter is used, all the angles defined at this point will be drawn, e.g. \drawAngle{O}. When used to reference one single defined angle, the direction doesn't matter. 
	E.g. \texttt{AOB} and \texttt{BOA} will return the same picture \drawAngle{AOB}. 
	When used to reference an angle composed of several defined angles, the name sould be given counterclockwise. 
	E.g. \texttt{\textbackslash drawAngle\{AOD\}} is \drawAngle{AOD} and \texttt{\textbackslash drawAngle\{DOA\}} is \drawAngle{DOA}.
	
	Can be called later using \texttt{\textbackslash angleAngleName}.
	
\subsubsection{\textbackslash drawAngleWithSides \{AngleName\}}

	\defineNewPicture{
	pair A, B, C, D;
	A := (1/2cm, 2cm);
	B := (0, 0);
	C := (3cm, 0);
	D := 1/2[A, C];
	byAngleDefine(A, B, D, byyellow, 1);
	byAngleDefine(D, B, C, byyellow, 0);
	byLineDefine(A, B, byred, 1, 0);
	byLineDefine(B, C, byblue, 0, 0);
	draw byNamedAngleResized();
	draw byNamedLineSeq(0)(AB, BC);
	} 

	Draws an angle and sections of its adjacent sides placed if angle portion style is not \texttt{0}. E.g., this angle \drawAngle{B} is drawn with \texttt{\textbackslash drawAngle\{B\}}, and this angle \drawAngleWithSides{B} is drawn with \texttt{\textbackslash drawAngleWithSides\{B\}}. 

	\texttt{AngleName}~— the same as in \ref{drawAngle}.
	
	Can be called later using \texttt{\textbackslash anglewithsidesAngleName}.
	
\subsubsection{\textbackslash drawPolygon[verticalAlignment][PolygonNewName] \{Poly\-gon\-Na\-me\}}

	Draws a polygon.

	\texttt{verticalAlignment}~— optional vertical alignment declaration. \texttt{middle} to align the picture with the middle of the line, anything else for bottom alignment.

	\texttt{PolygonNewName}~— optional polygon name. 
	
	\texttt{PolygonName}~— name of the polygon to reference in the main diagram. 
	
	If a name is given, can be called later using \texttt{\textbackslash PolygonNewName}, otherwise~— \texttt{\textbackslash polygonPolygonName}. 
	
\subsubsection{\textbackslash drawCircle[verticalAlignment][scaleFactor]\{CircleName\}}

	Draws a circle.

	\texttt{verticalAlignment}~— optional vertical alignment declaration. \texttt{middle} to align the picture with the middle of the line, anything else for bottom alignment.
	
	\texttt{scaleFactor}~— optional scale factor for the circle to replace the default offspring picture scale factor. 
	
	\texttt{CircleName}~— name of the circle to reference in the main diagram. 
	
	Can be called later using \texttt{\textbackslash circleCircleName}.
	
\subsubsection{\textbackslash drawArc[verticalAlignment][scaleFactor]\{ArcName\}}

	Draws an arc.

	\texttt{verticalAlignment}~— optional vertical alignment declaration. \texttt{middle} to align the picture with the middle of the line, anything else for bottom alignment.
	
	\texttt{scaleFactor}~— optional scale factor for the arc to replace the default offspring picture scale factor. 
	
	\texttt{ArcName}~— name of the arc to reference in the main diagram. 
	
	Can be called later using \texttt{\textbackslash arcCircleName}.
	
\subsubsection{\textbackslash drawLine[verticalAlignment][LineNewName]\{LineName\}}

	Draws a line.

	\texttt{verticalAlignment}~— optional vertical alignment declaration. \texttt{middle} to align the picture with the middle of the line, anything else for bottom alignment.
	
	\texttt{LineNewName}~— optional line name. 
	
	\texttt{LineName}~— name of the line to reference in the main diagram. 
	
	If a name is given, can be called later using \texttt{\textbackslash LineNewName}, otherwise~— \texttt{\textbackslash lineLineName}. 
	
\subsubsection{\textbackslash drawPointM\{PointName\}}

	\defineNewPicture{
	pair A, B, C, D;
	A := (0, 0);
	B := dir(15)*cm;
	C := B rotated 120;
	D := C rotated 120;
	byLineDefine(A, B, byred, 0, 0);
	byLineDefine(A, C, byyellow, 0, 0);
	byLineDefine(A, D, byblue, 0, 0);
	draw byNamedLine(AD);
	draw byNamedLineSeq(0)(AB,AC);
	draw byPointMark(A,  byblack, 1);
	}	

	Draws a point, depicted as a small circle \drawPointM{A}.
	
	\texttt{PointName}~— name of the point to reference in the main diagram. 
	
	Can be called later using \texttt{\textbackslash pointmPointName}. 

\subsubsection{\textbackslash drawPointL[verticalAlignment][LinesToOmit]\{PointName\}}\label{drawPointL}

	Draws a point, depicted as line segments starting/ending in it \drawPointL{A}. Only the lines which were actually drawn, not just defined, are used. Line segments' length is controlled by \texttt{pointLinesSize} \ref{pointLinesSize}.

	\texttt{verticalAlignment}~— optional vertical alignment declaration. \texttt{middle} to align the picture with the middle of the line, anything else for bottom alignment.
	
	\texttt{LinesToOmit}~— a comma-separated list lines, segments of which not to draw. 
	
	\texttt{PointName}~— name of the point to reference in the main diagram. 
	
	If a list of lines to omit is given, can be called later using \texttt{\textbackslash pointl\-Point\-Name\-Minus\-Lines\-To\-Omit}, otherwise~— \texttt{\textbackslash pointlPointName}. 

\subsubsection{\textbackslash drawPoint[verticalAlignment][LinesToOmit]\{PointName\}}

	Draws a point, depicted as line segments starting/ending in it with a point mark if defined \drawPoint{A}. Only the lines which were actually drawn, not just defined, are used.

	Arguments are the same as in \texttt{drawPointL} \ref{drawPointL}.
	
	If a list of lines to omit is given, can be called later using \texttt{\textbackslash point\-Point\-Name\-Minus\-Lines\-To\-Omit}, otherwise~— \texttt{\textbackslash pointPointName}. 

%\drawMagnitude

\bibliographystyle{plain}
\bibliography{byrne-latex}

\end{document}